It sounds like schools that require CSS Profile and NCP financials are likely to be unaffordable. Schools are unlikely to approve an NCP waiver as dad is paying child support. If dad’s new spouse works, their income and assets would also be included on CSS Profile (but again, I understand dad won’t fill this out/contribute $ to the twins education).
OP is also correct about coming FAFSA changes. OP can do FAFSA manually to figure out each twin’s EFC. This is just a draft document, so could change: https://fsapartners.ed.gov/sites/default/files/2022-11/202425DraftStudentAidIndexSAIandPellGrantEligibilityGuide.pdf